Question

A rectangular picture frame is 6 inches wide and 10 inches tall. You want to make the area 7 times as large by increasing the length and width by the same amount. Find the number of inches by which each dimension must be increased. Round to the nearest tenth.

Answer 1

12.6 inches

Explanation:

You want the increase in each dimension necessary to make a 6" by 10" frame have an area that is 7 times as much.

Area

The area of the original frame is ...

A = LW

A = (10 in)(6 in) = 60 in²

If each dimension is increased by x inches, the new area will be ...

A = (x +10)(x +6) = x² +16x +60 . . . . . square inches

We want this to be 7 times the area of 60 square inches:

x² +16x +60 = 7(60)

Solution

Subtracting 60, we get ...

x² +16x = 360

Completing the square, we have ...

x² +16x +64 = 424 . . . . . . . add 64

(x +8)² = ±2√106 ≈ ±20.6

x = 12.6 . . . . . . . . subtract 8; use only the positive solution

Each dimension must be increased by 12.6 inches to make the area 7 times as large.